Originally Posted by: pydrapeau
A432 is also knowned as Verdi tuning. Feel free to think anything you want, it's not about magic or cure cancer, I just like the mathematical fact that every note of the scale gets a round number C256, D288, E324, F342, G384, A432, B484.
How does this matter? So, mathematically speaking, the scientific pitch, philosophical pitch, or whatever you want to call it (it goes by several different names) just...what...it makes it easy to descrive what a C should be tuned to and that constitutes a reason to change the current standard we use today?
I think we need to keep a level head about this. Be logical about WHY we are looking to change what is considered a widely used standard in the world today, even tho many articles proclaiming 432 is the answer to saving the world from war and curing cancer also continue to claim that 440 middle A tuning is not a standard when in fact, it is. Every tuner, by default, out of the box defaults to 440 tuning. Unless specifically requested by the composer, instruments are tuned to the 440 tuning as a default.
'I just like even numbers' is also bizarre because in reality, what you are asking for is to move the 'whole numbers' from A to C, which will result in music being just shy of half a step in pitch lower than what it is today but otherwise, has no noticeable difference in sound..
If we are going to be technical about it, Verdi tuning doesnt even use a middle A at 432, its actually closer to 430.5 Hz.
Is it an interesting exercise from an academic perspective? Perhaps. My paper that Ill be turning in early December deals with tuning methods and this entire 432 hz phoenominon.
What I have come to realize as Ive begun outlining and sourcing my paper is two things.
1. You will never please everyone. There are people pushing for Verdi / scientific tuning, there are people pushing for 432 hz tuning, and several others that dont come to the top of my head at the moment. Most of the reasons, are hocus pocus or that it 'feels good' - in that, not that the music is better but that it 'feels good' to say everything has an even number, or odd number, or no decimal points, or whatever. Actually, I havent come across a reason yet that would suggest to me a good logical reason as to why we should change except choral arrangements would be easier to sing, and even then, I would argue the composer should transpose down half a step if he is concerned about straining his singers voices.
2. Music will never be 100% mathematically perfect with nice round numbers. Why? Because our hearing is not 100% mathematically perfect. Tune a piano to be mathematically pitch perfect and what youll get is sharp sounding notes in the high end and flat sounding notes in the low end. It is why we use the system we use today, it is a compromise, probably as close a compromise as we can get to avoid things sounding out of tune. Yes, the system we use today isnt perfect. Listen to a note and its third (a C and an E for example) and you'll hear 'beats' in the sound because the C and E are slightly out of tune such that we can play a note and its fifth (a C and a G for example) and have a near perfect harmony. We can play a note an octave apart and have no 'beats'. Our tuning system we use today emphasizes the same priorities that Bach described. Octaves, then fifths, then thirds, that should be the priority. Bach was annoyed about the tuning methods that were used and yelled at his organ engineer every time he played a note and its fifth, it was even worse when he played a triad that included a fifth and he would yell at his organist and complain constantly about it, thats why we have what we have today.
I will even go so far as to say that music will never be 100% mathematically perfect because math is not 100% perfect. There are numerous examples I can give to prove this, but Ill give you two to ponder on.
What happens when you multiply 1/3 times 3? You should get 1. (1/3 * 3 = 1 OR 1/3 + 1/3 + 1/3 = 1). Now convert 1/3 to a decimal and multiply by 3. You get .9 repeating (.3 repeating * 3 = .9 repeating OR 3 repeating + .3 repeating + .3 repeating = .9 repeating), not 1, as you would get if multiplying the fraction.
Can anyone give me the square root of a negative number? Any negative number? It doesnt exist! In math, we had to make something up and call it an imaginary number (normally assigned to the variable 'i', although in engineering, they use 'j' for reasons I cant get into here).
The square root of a number, that is, a number when multiplied by itself equals the number we are looking for the square root of. The easiest way to demonstrate this is -1. The square root cant be -1 since two negatives when multiplied equal a postive and two positives equal a positive, so, we define the square root of -1 as -1i or 1i, depending on which mathemitician you ask (the i meaning, 1 times a number we cant define).
As another interesting side note to think about, if looking for the even root of a number, it actually is 2 numbers, positive and negative. The square root of 4 is actually 2 and -2 (2*2=4 and -2*-2=4). The root of 16 with an index of 4 is 2 and -2. Anyway, just mentioning this as food for thought since most people probably never thought about it before :). But I digress...
Few things in life are perfect, music is no exception. Technically, sound to be more precise, is not perfect.